Density-functional theory (DFT) and QCISD(T) calculations have been used to investigate the mechanism of cyclodimerisation and cyclotrimerisation of acetylene at a cyclopentadienyl-CoI centre. In contrast to earlier investigations, we find that the most favourable mechanism for the formation of benzene involves the insertion of an acetylene molecule into a Co–C bond of the well known cobaltacyclopentadienyl intermediate. The product of this reaction then undergoes very facile ring-closure to benzene. This mechanism is found to be more favourable than the concerted Diels–Alder path, which is the highest in energy of the three mechanisms considered. The remaining reaction path involves initial addition of an acetylene molecule to the cyclopentadienyl ligand followed by rearrangement to give a 1,3,5-hexatrien-1-ylcyclopentane ligand system, which cleaves to give benzene and cyclopentadienyl ligands. Spin crossovers between the singlet and triplet states are found for the ring-closure of the cobaltacyclopentadienyl intermediate to give a cyclobutadiene complex and for the concerted Diels–Alder process. These spin crossovers and the reaction mechanisms in general are rationalised in terms of the concept of electron-transfer catalysis.